{"id":"https://openalex.org/W1501637923","doi":"https://doi.org/10.1137/140970951","title":"ATLAS: A Geometric Approach to Learning High-Dimensional Stochastic Systems Near Manifolds","display_name":"ATLAS: A Geometric Approach to Learning High-Dimensional Stochastic Systems Near Manifolds","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W1501637923","doi":"https://doi.org/10.1137/140970951","mag":"1501637923"},"language":"en","primary_location":{"id":"doi:10.1137/140970951","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140970951","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1404.0667","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017471297","display_name":"Miles Crosskey","orcid":"https://orcid.org/0000-0002-0625-7718"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Miles Crosskey","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5089371996","display_name":"Mauro Maggioni","orcid":"https://orcid.org/0000-0003-3258-9297"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mauro Maggioni","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017471297"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00062292,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"1","first_page":"110","last_page":"156"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9839000105857849,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9818999767303467,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/microscale-chemistry","display_name":"Microscale chemistry","score":0.9787342548370361},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6870803236961365},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6215397715568542},{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.6164820194244385},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.573462188243866},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5185016393661499},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4886015057563782},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4517098367214203},{"id":"https://openalex.org/keywords/multiscale-modeling","display_name":"Multiscale modeling","score":0.43117737770080566},{"id":"https://openalex.org/keywords/rendering","display_name":"Rendering (computer graphics)","score":0.42477336525917053},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.3774288594722748},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2982741594314575},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18250858783721924},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11774638295173645}],"concepts":[{"id":"https://openalex.org/C179428855","wikidata":"https://www.wikidata.org/wiki/Q1069216","display_name":"Microscale chemistry","level":2,"score":0.9787342548370361},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6870803236961365},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6215397715568542},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.6164820194244385},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.573462188243866},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5185016393661499},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4886015057563782},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4517098367214203},{"id":"https://openalex.org/C141123601","wikidata":"https://www.wikidata.org/wiki/Q6935072","display_name":"Multiscale modeling","level":2,"score":0.43117737770080566},{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.42477336525917053},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.3774288594722748},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2982741594314575},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18250858783721924},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11774638295173645},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/140970951","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140970951","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1404.0667","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1404.0667","pdf_url":"https://arxiv.org/pdf/1404.0667","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:1501637923","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1404.0667","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.751.7582","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.751.7582","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1404.0667.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1404.0667","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1404.0667","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1404.0667","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1404.0667","pdf_url":"https://arxiv.org/pdf/1404.0667","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7699999809265137,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G5522876257","display_name":null,"funder_award_id":"0847388","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G7088870815","display_name":null,"funder_award_id":"1265920","funder_id":"https://openalex.org/F4320337393","funder_display_name":"Division of Chemistry"},{"id":"https://openalex.org/G8803770088","display_name":null,"funder_award_id":"N00014-12-1-0601","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320337393","display_name":"Division of Chemistry","ror":"https://ror.org/01ar8dr59"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W1519654970","https://openalex.org/W1524094700","https://openalex.org/W1545319692","https://openalex.org/W1562856242","https://openalex.org/W1572902284","https://openalex.org/W1590943005","https://openalex.org/W1595132914","https://openalex.org/W1673352269","https://openalex.org/W1852328762","https://openalex.org/W1970592267","https://openalex.org/W1971725855","https://openalex.org/W1976660933","https://openalex.org/W1978261861","https://openalex.org/W1979070806","https://openalex.org/W1983132551","https://openalex.org/W1987236926","https://openalex.org/W1987924751","https://openalex.org/W2011242225","https://openalex.org/W2012306680","https://openalex.org/W2021270935","https://openalex.org/W2025335914","https://openalex.org/W2032227660","https://openalex.org/W2053348581","https://openalex.org/W2063532964","https://openalex.org/W2064556178","https://openalex.org/W2064733273","https://openalex.org/W2067752346","https://openalex.org/W2068643094","https://openalex.org/W2070460788","https://openalex.org/W2073644805","https://openalex.org/W2077412035","https://openalex.org/W2081760211","https://openalex.org/W2092144432","https://openalex.org/W2096450582","https://openalex.org/W2111818440","https://openalex.org/W2117684310","https://openalex.org/W2119489903","https://openalex.org/W2133296809","https://openalex.org/W2136958763","https://openalex.org/W2139139723","https://openalex.org/W2140565568","https://openalex.org/W2142506069","https://openalex.org/W2147848673","https://openalex.org/W2160341881","https://openalex.org/W2167077362","https://openalex.org/W2227023074","https://openalex.org/W2229640315","https://openalex.org/W2405566609","https://openalex.org/W2802739963","https://openalex.org/W2964012263","https://openalex.org/W2965497096","https://openalex.org/W3124025666","https://openalex.org/W4213367101"],"related_works":["https://openalex.org/W2165067994","https://openalex.org/W2952667960","https://openalex.org/W2471063652","https://openalex.org/W3174635800","https://openalex.org/W3015646172","https://openalex.org/W2513334","https://openalex.org/W2989765054","https://openalex.org/W2975251257","https://openalex.org/W2788823228","https://openalex.org/W2798624337","https://openalex.org/W2802436438","https://openalex.org/W3043183264","https://openalex.org/W2786232134","https://openalex.org/W2096170434","https://openalex.org/W3170693999","https://openalex.org/W3012139881","https://openalex.org/W2135078484","https://openalex.org/W2963805841","https://openalex.org/W2767540877","https://openalex.org/W3104016817"],"abstract_inverted_index":{"When":[0],"simulating":[1],"multiscale":[2],"stochastic":[3,12],"differential":[4],"equations":[5],"(SDEs)":[6],"in":[7,115,147],"high-dimensions,":[8],"separation":[9],"of":[10,31,37,57,145,164,174,185,205,218],"timescales,":[11,48],"noise,":[13],"and":[14,29,45,68,117,132,162,196,211],"high-dimensionality":[15],"can":[16,155],"make":[17],"simulations":[18,104],"prohibitively":[19],"expensive.":[20],"The":[21,119,151],"computational":[22],"cost":[23],"is":[24,73,140],"dictated":[25],"by":[26,51,70],"microscale":[27,67,103,126,180,224],"properties":[28],"interactions":[30],"many":[32,60],"variables,":[33],"while":[34],"the":[35,42,63,66,125,141,148,172,179,183,186,203,206,212,216,223],"behavior":[36],"interest":[38,146],"often":[39,49],"occurs":[40],"at":[41,46],"macroscale":[43,69,94,109,153,188],"level":[44],"large":[47],"characterized":[50],"few":[52],"important,":[53],"but":[54],"unknown,":[55],"degrees":[56],"freedom.":[58],"For":[59],"problems":[61],"bridging":[62],"gap":[64],"between":[65],"direct":[71],"simulation":[72],"computationally":[74],"infeasible.":[75],"In":[76],"this":[77],"work":[78],"we":[79,209],"propose":[80],"a":[81,87,128,133],"novel":[82],"approach":[83],"to":[84,105,182],"automatically":[85],"learn":[86,106],"reduced":[88,149],"model":[89,154],"with":[90],"an":[91],"associated":[92],"fast":[93,160,207],"simulator.":[95,189,225],"Our":[96],"unsupervised":[97],"learning":[98,120],"algorithm":[99,121],"uses":[100],"short":[101,175,219],"parallelizable":[102],"provably":[107],"accurate":[108],"SDE":[110],"models,":[111],"which":[112,139],"are":[113],"continuous":[114],"space":[116],"time.":[118],"takes":[122],"as":[123,198,200],"input":[124],"simulator,":[127],"local":[129],"distance":[130],"function,":[131],"homogenization":[134],"spatial":[135],"or":[136],"temporal":[137],"scale,":[138],"smallest":[142],"time":[143],"scale":[144],"system.":[150],"learned":[152,187],"then":[156],"be":[157],"used":[158],"for":[159],"computation":[161],"storage":[163],"long":[165],"simulations.":[166],"We":[167,190],"prove":[168],"guarantees":[169],"that":[170],"relate":[171],"number":[173,217],"paths":[176,220],"requested":[177,221],"from":[178,222],"simulator":[181],"accuracy":[184,204],"discuss":[191],"various":[192],"examples,":[193],"both":[194],"low-":[195],"high-dimensional,":[197],"well":[199],"results":[201],"about":[202],"simulators":[208],"construct,":[210],"model's":[213],"dependency":[214],"on":[215]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}